progress toward stabilization of low internal inductance spherical torus plasmas in nstx s.a....

Progress Toward Stabilization of Low Internal Inductance Progress Toward Stabilization of Low Internal Inductance Spherical Torus Plasmas in NSTXSpherical Torus Plasmas in NSTX

S.A. Sabbagh1, J.W. Berkery1, J.M. Bialek1, S.P. Gerhardt2, R.E. Bell2, O.N. Katsuro-Hopkins1, J.E.

Menard2, R. Betti2,3, L. Delgado-Aparicio2, D.A. Gates2, B. Hu3, B.P. LeBlanc2, J. Manickam2, D.

Mastrovito2, J.K. Park2, Y.S. Park1, K. Tritz4

1Department of Applied Physics, Columbia University, NY, NY2Plasma Physics Laboratory, Princeton University, Princeton, NJ

3University of Rochester, Rochester, NY 4Johns Hopkins University, Baltimore, MD

52nd APS DPP Meeting

November 9th, 2010

Chicago, Illinois

College W&MColorado Sch MinesColumbia UComp-XGeneral AtomicsINELJohns Hopkins ULANLLLNLLodestarMITNova PhotonicsNew York UOld Dominion UORNLPPPLPSIPrinceton UPurdue USandia NLThink Tank, Inc.UC DavisUC IrvineUCLAUCSDU ColoradoU MarylandU RochesterU WashingtonU Wisconsin

Culham Sci CtrU St. Andrews

York UChubu UFukui U

Hiroshima UHyogo UKyoto U

Kyushu UKyushu Tokai U

NIFSNiigata UU Tokyo

JAEAHebrew UIoffe Inst

RRC Kurchatov InstTRINITI

KBSIKAIST

POSTECHASIPP

ENEA, FrascatiCEA, Cadarache

IPP, JülichIPP, Garching

ASCR, Czech RepU Quebec

NSTXNSTX Supported by

V1.8

NSTXNSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low li Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.) 2November 9th, 2010

NSTX is Addressing Global Stability Needs for Maintaining Low li, High Beta Plasmas for Fusion Applications

Motivation Achieve high N with sufficient physics understanding to allow

confident extrapolation to spherical torus applications (e.g. ST Component Test Facility, ST-Pilot plant, ST-DEMO)

Sustain target N of ST applications with margin to reduce risk Leverage unique ST operating regime to test physics models, apply

to ITER

Physics Research Addressed in this Talk Plasma operation at low plasma internal inductance (li) Resistive wall mode (RWM) destabilization at high plasma rotation Combined control systems to maintain <N>pulse at varied

RWM active control enhancements / advances at low li Multi-mode RWM spectrum in high N plasmas

NP9.00011 PengUP9.00006 Hawryluk


Future ST fusion applications will have high elongation, broad current profiles, high normalized beta

Broad current profiles (low li) consistent with high bootstrap current fraction; important to maintain high elongation

Demonstrating / understanding kink / RWM stability at low li is important

ST-Pilot (Qeng = 1)FNSF / ST-CTF

li = 0.47, = 3.2 R = 2.23 m, A = 1.7 Ip = 16 MA, Bt = 2.4T

N = 5.2, t = 30%

J. Menard, et al., IAEA FEC 2010 Paper FTP/2-2

Y.K.M. Peng, et al., PPCF 47 (2005) B263

Current Profile (MA/m2)

1 2 3 4

2.0

1.5

1.0

0.5

0.0R(m)


RWM active stabilization coils

RWM poloidal sensors (Bp)

RWM radial sensors (Br)

Stabilizerplates

High beta, low aspect ratio R = 0.86 m, A > 1.27 Ip < 1.5 MA, Bt = 5.5 kG

t < 40%, N < 7.4

Copper stabilizer plates for kink mode stabilization

Midplane control coils n = 1 – 3 field correction,

magnetic braking of by NTV n = 1 RWM control

Varied sensor combinations used for RWM feedback 48 upper/lower Bp, Br

NSTX is a spherical torus equipped for passive and active global MHD control, application of 3D fields


Operation aims to produce sustained low li and high pulse-averaged N

Next-step ST fusion devices aim to operate at low li (high bootstrap current fraction > 50%) and high N

Focus on sustained low li and high <N>pulse

N vs. li (maximum values) N vs. li (pulse-averaged values)

N (

ma

xim

um)

ST-CTF

ST-DEMO (ARIES-ST)

ST-CTF

< N

>p

ulse

ST-Pilot ST-Pilot

ST-DEMO (ARIES-ST)

Recent years with “routine” n = 1 RWM feedback (red)


0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8


N vs. li (maximum values)

N

N/li is a common parameter to evaluate global stability Kink/ballooning and

RWM stability

Significant increase in maximum N/li Upper limit now

between 13 - 14

li

N/li 13 12 11 1014




N

N/li is a common parameter to evaluate global stability Kink/ballooning and

RWM stability

Significant increase in maximum N/li Upper limit now

between 13 - 14

At sufficiently low li, “current driven kink” limit exists Plasma unstable

without conducting wall, or FB control, at any N value

li

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

N/li 13 12 11 1014

“current-drivenkink limit”(schematic)


Ideal no-wall stability limit decreases for low li plasmas


N

Examine high plasma current, Ip >= 1.0MA, high non-inductive fraction ~ 50%

Ideal n = 1 no-wall stability computed for discharge trajectory Plasma exceeds

no-wall limit at N = 3.4, li = 0.51

li

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

N/li 13 12 11 1014

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8




N

Examine high plasma current, Ip >= 1.0MA, high non-inductive fraction ~ 50%

Ideal n = 1 no-wall stability computed for discharge trajectory Plasma exceeds no-

wall limit at N = 3.4, li = 0.51

Adding trajectories yields N/li = 6.7 for li = 0.38 – 0.5

Significantly lower than usual no-wall limit at higher li (N = 4.3)

li

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

N/li 13 12 11 1014

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

N/li = 6.7

ST-CTFST-Pilot


Experiments aimed to produce sustained low li and high N at high plasma current


N

High Ip >= 1.0MA, high non-inductive fraction ~ 50%

Initial experiments Yielded low li Access high N/li High disruption

probability

Instabilities leading to disruption Unstable RWM

• 48% of cases run Locked tearing

modesli

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

N/li 13 12 11 1014

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

N/li = 6.7

Unstable RWM

Stable / controlled RWM

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8


0123456

-

020406080100

Tesla

0

100

200

300

Degree

s

0.57 0.575 0.580 0.585 0.590 0.595 0.600Seconds

-30-20-1001020

11

Low plasma rotation level (~ 1% Alfven) is insufficient to ensure RWM stability, which depends on profile

RWM unstable plasma Instability occurs at relatively high rotation level,

and not at highest N (4.7)

RWM stable plasma MHD spectroscopy: increased resonant field

amplification (RFA) indicates reduced stability Plasma moves to more stable regime (lower

RFA) at lower rotation (N up to 6.5)

unstable RWM

RWM rotation

t(s)0.57 0.58 0.59 0.60

642

8040

0300200

N

Bpun=1(G)

0

Bpun=1(deg)

137722

RWM unstable plasma

MHD spectroscopy (stable plasma)

stable

140102

(140102)

Plasma rotation

100

Stable up to N = 6.5

0

1 1

(137722)

unstable

t(s)

n=1 tracer field

n=3 braking


ˆˆ2

3ˆˆ2

5**

deiil

iW

EeffbD

ETN

K

Reason: simple critical threshold stability models do not fully describe RWM marginal stability in NSTX

Kinetic modification to ideal MHD growth rate Trapped / circulating ions, trapped electrons, etc.

Energetic particle (EP) stabilization

Stability depends on

Integrated profile: resonances in WK (e.g. ion precession drift)

Particle collisionality, EP fractionTrapped ion component of WK (plasma integral)

Energy integral

Kb

Kw WW

WW

collisionality

profile (enters through ExB frequency)

Hu and Betti, Phys. Rev. Lett 93 (2004) 105002.

Sontag, et al., Nucl. Fusion 47 (2007) 1005.

precession drift bounce

Modification of Ideal Stability by Kinetic theory (MISK code) investigated to explain experimental RWM stabilization

BP9.00057 J. Berkery, et al.


NSTX 121083

unstable

(mar

gina

l sta

bilit

y)

unstable

Pre

cess

ion

dri

ft

reso

nan

ce s

tab

iliza

tio

n

Bo

un

ce/t

ran

sit

reso

nan

ce s

tab

iliza

tio

n

Marginal stability

eff/

exp

(ma

rgin

al s

tab

ility

)

13

MISK calculations consistent with RWM destabilization at intermediate plasma rotation; stability altered by

collisionality

Destabilization appears between precession drift resonance at low , bounce/transit resonance at high

w contours vs. ν and

/exp (marginal stability)

J.W. Berkery, et al., PRL 104 (2010) 035003 S.A. Sabbagh, et al., NF 50 (2010) 025020


NSTX 121083

unstable

(mar

gina

l sta

bilit

y)

unstable

Pre

cess

ion

dri

ft

reso

nan

ce s

tab

iliza

tio

n

Bo

un

ce/t

ran

sit

reso

nan

ce s

tab

iliza

tio

n

Pla

sma

evo

luti

on

eff/

exp

(ma

rgin

al s

tab

ility

)

14


collisionality






NSTX 121083

unstable

(mar

gina

l sta

bilit

y)

unstable

Pre

cess

ion

dri

ft

reso

nan

ce s

tab

iliza

tio

n

Bo

un

ce/t

ran

sit

reso

nan

ce s

tab

iliza

tio

n

Pla

sma

evo

luti

on

Marginal stability

eff/

exp

(ma

rgin

al s

tab

ility

)

15


collisionality


Destabilization moves to increased as decreases


instability

(experiment)




MISK calculations show reduced stability in low li target plasma as is reduced, RWM instability is approached

Stability evolves li increases in time as RWM

instability is approached, but remains low (li = 0.42)

MISK computation shows plasma to be stable at time of minimum li

Region of reduced stability vs. found before RWM becomes unstable (li = 0.49)

• Co-incident with a drop in edge density gradient – reduces kinetic stabilization

MISK application to ITER (advanced scenario IV) RWM unstable at expected rotation Only marginally stabilized by

alphas at N = 3

140132, t = 0.704s

stable

unstable

- BP9.00057 J. Berkery, et al.- Also, see poster for detail

experiment

RWM stability vs. (contours of w)

2.0

1.0

/exp

thermalw/fast particles


0123456

0123456

-600-400-200

0200400600

02468101214

0 0.2 0.4 0.6 0.8 1.0 1.2sec

051015202530

135468135513

Shots:

N feedback combined with n = 1 RWM control to reduce N fluctuations at varied plasma rotation levels

Prelude to control Reduced by

n = 3 braking is compatible with N FB control

Steady N established over long pulse independent of over a large range

Radial field sensors recently added to n = 1 feedback

135468135513

0.80.4 0.6 1.0 1.2t(s)

0.20.0

N

2

46

I RW

M-6 (

kA) 0.6

0

2

46

-0.6

PN

BI (

MW

) ~

q=

2

(kH

z) c

ore

(kH

z)

48

12

30

10

n = 3 brakingn = 1 feedback

0

20

0

q ~ 2 rotation

Core rotation

n = 3 errorcorrection


01

2

3

4

56

-

0

0.2

0.4

0.6

0.8

-

02

4

6

8

1012

*

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Seconds

01234567

Tesla

140124140125140126140127

Shots:

RWM Br sensor n = 1 feedback phase variation shows clear settings for improved feedback when combined with Bp sensors

Recent corrections to Br sensors improve measurement of plasma response Removed significant

direct pickup of time-dependent TF intrinsic error field

Positive/negative feedback produced at theoretically expected phase values

Adjustment of Bp sensor feedback phase from past value further improved control performance

n = 1 BR + Bp feedback(Bp gain = 1, BR gain = 1.5)

Brn = 1 (G)

N

li

~q=2 (kHz)

Br FB phase = 0o

Br FB phase = 225o

Br FB phase = 90o

140124140125140126140127

Br FB phase = 180o

t (s)


01

2

3

4

56

-

0

0.2

0.4

0.6

0.8

-

02

4

6

8

1012

*

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Seconds

01234567

Tesla

140124140122139516

Shots:

RWM BR sensor feedback gain scan shows significantly reduced n= 1 radial error field

New Br sensor feedback gain scan on low li plasmas Highest gain

attempted (1.5) most favorable

Br feedback constrains slow (10’s of ms) n = 1 radial field growth Addition of n = 1

BR sensors in feedback prevents disruptions when |Br

n=1| ~ 9G; better sustains plasma rotation

Br Gain = 1.50

Br Gain = 1.0

n = 1 BR + Bp feedback(Bp gain = 1)

140124140122139516

No Br feedback

t (s)

Brn = 1 (G)

N

li

~q=2 (kHz)


01234567

-

0

100

200

300

400

500

amperes

01234567

Tesla

0 0.2 0.4 0.6 0.8 1.0Seconds

01234567

128693139347140137

Shots:

Use of combined RWM sensor n= 1 feedback yields best reduction of n = 1 field amplitude / improved stability

Combination of DC error field correction, n = 1 feedback n = 3 DC error

field correction alone more subject to RWM instability

n = 1 Bp sensor fast RWM feedback sustains plasma

Addition of n = 1 BR sensors in feedback reduce the combined Bp and Br n = 1 field to 1 – 2 G level

(Bp+ Br)n = 1 (G)

N

Feedback current (A)

+ n = 1 Bp feedback

128693139347140137

n = 3 correction alone(RWM-induced disruption)

t (s)

+ n = 1 Bp + BR feedback

Brn = 1 (G)

+ n = 1 Bp feedback

+ n = 1 Bp + BR feedback


Improvements in stability control techniques significantly reduce unstable RWMs at low li and high N

N

High Ip >= 1.0MA

Latest experiments Yielded low li Access high N/li Significantly

reduced disruption probability due to unstable RWM

• 14% of cases with N/li > 11

• Much higher probability of unstable RWMs at lower N, N/li li

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

N/li 13 12 11 10

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

14

N/li = 6.7

Unstable RWM

Stable / controlled RWM

0

1

2

3

4

5

6

7

8

0.0 0.2 0.4 0.6 0.8

New RWM State SpaceControllerResults


BR sensors added: longest pulse plasmas, high performance (NOTE: COMBINE with a bN/li vs. pulse plot

139347139517139518139519

Bpn = 1 (G)

Ip (MA)

Combined use of Bp and Br sensor feedback is best Cases ran

with MIU compens. on, or off

Continued use of feedback has MIU compens. on with good result

Bp + BR feedback onBp sensors 180 deg FB phase(last run)

N

li

N/li

PLACEHOLDER


New RWM state space controller (RWMSC) implemented to sustain high N

Balancingtransformation

~3000+ states

Full 3-D model

…

RWMeigenfunction(2 phases,

2 states)

)ˆ,ˆ( 21 xx 3x̂ 4x̂ Nx̂truncate

State reduction (< 20 states)

Theoretical feedback performance ( = 0, 12 states)

Controller can compensate for wall currents Including mode-induced current

Potential to allow more flexible control coil positioning May allow coils to be moved

further from plasma, shielded Examined for ITER

- device R, L, mutual inductances- instability B field / plasma response- modeled sensor response

Katsuro-Hopkins, et al., NF 47 (2007) 11574.0 N

4.5 5.0 5.5 6.0 6.5 7.0 7.5100

101

102

103

104

(1

/s)

Proportional gain control limit

Passive growth

Idea

l Wal

l Lim

it

State

space

controller

(low input)

(high input)

4.0 N4.5 5.0 5.5 6.0 6.5 7.0 7.5

100

101

102

103

104

(1

/s)

100

101

102

103

104

(1

/s)


Passive growth

Idea

l Wal

l Lim

it

State

space

controller

(low input)

(high input)


RWM state space controller with 7 states improves match to sensors over entire evolution compared to 2 states

Bp UPPER Sensor Differences – 2 States

Sensor not functioning

137722

180 degreedifferences




RWM

Black: experiment Red: offline RWM state space controller



137722





RWM

Reasonable match to all Bp sensors during RWM onset, large differences later in evolution

Some 90 degree sensor differences not as well matched May indicate need for n = 2

eigenfunction state


RWM state space controller with 7 states improves match to sensors over entire evolution compared to 2 states



137722





RWM

Black: experiment Red: offline RWM state space controller



137722





RWM

Reasonable match to all Bp sensors during RWM onset, large differences later in evolution

Some 90 degree sensor differences not as well matched May indicate need for n = 2

eigenfunction state

Add Flip-Slide with calculation showing the effect

of the NBI port – significantly better match to one

of the 90 degree sensors


New RWM state space controller sustains high N, low li plasma

RWM state space feedback (12 states)

n = 1 applied field suppression Suppressed

disruption due to n = 1 field

Feedback phase scan Best feedback

phase produced long pulse, N = 6.4, N/li = 13

00.20.40.60.81.01.2

amperes

01234567

-

0246810

Tesla

0100200300400500

amperes

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4sec

02468

140037140035

Favorable FB phaseUnfavorable feedback phase

N

IRWM-4 (kA)

~q=2

(kHz)

Bpn=1 (G)

Ip (kA)

0.80.4 0.6 1.0 1.2t(s)0.20.0 1.4

1.00.5

06420840

400200

0

840

12

00.20.40.60.81.01.2

amperes

01234567

-

0246810

Tesla

0100200300400500

amperes

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4sec

02468

140037140035


N

IRWM-4 (kA)

~q=2

(kHz)

Bpn=1 (G)

Ip (kA)

0.80.4 0.6 1.0 1.2t(s)0.20.0 1.4

1.00.5

06420840

400200

0

840

12

Successful FirstExperiments

(See poster for detail)


0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15

Multi-mode RWM computation shows 2nd eigenmode component has dominant amplitude at high N in NSTX stabilizing structure

NSTX RWM not stabilized by Computed growth time consistent with

experiment 2nd eigenmode (“divertor”) has larger

amplitude than ballooning eigenmode

NSTX RWM stabilized by Ballooning eigenmode amplitude

decreases relative to “divertor” mode Computed RWM rotation ~ 41 Hz,

close to experimental value ~ 30 Hz ITER scenario IV multi-mode spectrum

Significant spectrum for n = 1 and 2

Bn from wall, multi-mode responseBn RWM multi-mode composition

ideal eigenmode number

Bn

ampl

itude

(ar

b)

t = 0.655s

mode 1

mode 2

2.01.00.0R(m)

1.0

-1.0

Z(m

)

2.0

0.0

-2.0

mode 3

133775

mode

1

mode

3

mode

2

Unstable

Stabilized by rotation

BP9.00059 J. Bialek, et al.; see poster for detailmmVALEN code

N = 6.1


NSTX is Addressing Global Stability Needs Furthering Steady Operation of High Performance ST Plasmas

Success in producing, and stabilizing plasmas with reduced li

Approaching conditions of ST fusion applications

RWM instability observed at intermediate plasma rotation correlates with kinetic stability theory Suggests the need for rotation control in future ST devices; evaluation of

energetic particle (EP) stabilization

Initial analysis of low li plasmas indicates similar stability dependence on

n = 1 RWM feedback control combined with N feedback control shows stability and regulation of high N at varied plasma rotation levels

Compatible with plasma rotation control by non-resonant 3D fields

New RWM state space controller sustains high N plasma

Potential for greater flexibility of RWM control coil placement in burning plasma devices

Computed multi-mode RWM spectrum at high N with 3D conducting structure shows significant amplitude in higher order eigenmode


Backup and Poster Slides


RWM state space controller sustains otherwise disrupted plasma caused by DC n = 1 applied field

n = 1 DC applied field Simple method to

generate resonant field amplication

Can lead to mode onset, disruption

RWM state space controller sustains discharge With control, plasma

survives n = 1 pulse n = 1 DC field

reduced Transients controlled

and do not lead to disruption

NOTE: initial run – gains NOT optimized

00.20.40.60.81.01.2

amperes

0123456

-

0246810

Tesla

0100200300400500

amperes

0 0.2 0.4 0.6 0.8 1.0sec

024681012

*

140025140026

Shots:

140025140026

Control applied

Control not applied

N

IRWM-4 (kA)

~q=2 (kHz)

t(s)

Bpn=1 (G)

Ip (kA)

NSTXNSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low li Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.) 31November 9th, 2010 31

ITER Advanced Scenario IV: RWM just reaches marginal stability by energetic particles with N = 3

Equilibrium With N = 3 (20% above n = 1

no-wall limit) Plasma rotation profile linear

in normalized poloidal flux

Plasma rotation effect Stabilizing precession drift

resonance weakly enhances stability near = 0.8

Polevoi

Energetic particle (EP) effect Alpha particles are required

for RWM stabilization at all Near RWM marginal stability

at ITER expected /total = 0.19 at =

Polevoi

MISK stability code


ITER Advanced Scenario IV: multi-mode RWM spectra computation shows significant ideal eigenfunction amplitude for several components

Z(m

)

-4

-2

0

2

4

6

4 6 8 10

ITERBnormalPLOTS2010

Z 1.00Z Bn#1@0 1Z Bn#3@0 1Z Bn#5@0 1

Z 1

.00

R 1.00

n = 2.6530 n=1

DDSO.EQDSK_ITER1.00S

-4

-2

0

2

4

6

4 6 8 10


Z 1.40Z Bn#1@0 1Z Bn#3@0 1Z Bn#5@0 1

Z 1

.40

R 1.40

n = 3.9170 n=1


N = 3.92n = 1

N = 2.65n = 1

-4

-2

0

2

4

6

4 6 8 10


n=2 Z 1.40n=2 Z Bn#1@0 1n=2 Z Bn#3@0 1n=2 Z Bn#5@0 1

n=

2 Z

1.4

0

n=2 R 1.40

n = 3.9170 n=2


N = 3.92n = 2

mode 1

4

-2

6

0

-4

2

R(m)4 6 8 10

Z(m

)

4

-2

6

0

-4

2

R(m)4 6 8 10

Z(m

)

4

-2

6

0

-4

2

R(m)4 6 8 10

0 3 9 126 15

1.0

0.8

0.6

0.4

0.2

0.0

mode 2mode 3

mode 1mode 2mode 3

mode 1mode 2mode 3


Bn

ampl

itude

(ar

b)

Multi-mode spectrum

N = 2.65n = 1

0 3 9 126 15

1.0

0.8

0.6

0.4

0.2

0.0


mmVALEN

0 3 9 126 15

1.0

0.8

0.6

0.4

0.2

0.0


Multi-mode

spectrum

Multi-mode

spectrum

N = 3.92n = 1

N = 3.92n = 2

Nno-wall = 2.5


ABSTRACT

Steady-state spherical torus plasmas for fusion applications, such as a component test facility or demonstration power plant, target operation with high non-inductive current fraction. These broad current profile targets have low values of plasma internal inductance, l i, less than 0.4, near to the lower end of present NSTX operation. A key significance of this operation is that it approaches the purely current-driven ideal kink limit, which by definition exceeds the no-wall stability limit for all values of plasma normalized pressure (beta). In this regime, passive or active kink and resistive wall mode (RWM) stabilization is critical. Experiments on NSTX have recently approached this condition, evidenced by a significant reduction of the n = 1 no-wall stability limit computed by DCON. This limit drops from normalized beta of 4.2 – 4.6 at l i ~ 0.6, to 3.4 at li ~ 0.5, to below 2.8 for li ~ 0.4. Nevertheless, passive and active RWM control has produced high toroidal beta up to 28 percent, and normalized beta up to 6.5 (nearly double the no-wall limit), closely following a record normalized beta to li ratio of 13 between li = 0.4 - 0.5. Non-inductive current fraction reaches 0.5 in these high normalized current plasmas. However, the disruption probability of these plasmas increases significantly, with about half of the discharges suffering terminating instabilities. Alteration of n = 1 RWM control system parameters, plasma rotation profile, and the role of beta feedback is examined to potentially improve mode stability. Ion precession drift and bounce frequency resonance stabilization is examined for these plasmas and compared to the identified stabilization reduction at intermediate plasma rotation and higher l i [1,2].

[1] J.W. Berkery, et al., Phys. Rev. Lett. 104, 035003 (2010)

[2] S.A. Sabbagh, et al., Nucl. Fusion 50 , 025020 (2010)

*Work supported by U.S. DOE Contracts DE-FG02-99ER54524 and DE-AC02-09CH11466.


Work slides


Slide ToDos

To Do Update words on database slides Add n = 1 no-wall limit “extension” on n = 1 line in database plot Add database slide showing the results of IMPROVEMENTS to

control systems, etc. – can be an intro to the next sections of talk. Illustrate reduced disruptivity here best you can!

• Think about how best to do this in the short-term

• Use XP1023 runs from (some 7/29), 8/3, 8/19, 9/24, other runs, fiducials

• NOTE: Runs on 4/13 and 4/15 mostly were lower betaN Add database slide(s) as time allows (<betaN>, <BetaT> vs. pulse) Update Bp feedback phase slide Update (combine?) Br gain / phase variation slide Include key PHYSICS of the change in RWM mode dynamics in the

waveform slides (see EXCEL spreadsheet for this) Update VALEN model of 3d conducting structure


ABSTRACT (update to include new control/stability, RWMSC)

Steady-state spherical torus plasmas for fusion applications, such as a component test facility or demonstration power plant, target operation with high non-inductive current fraction. These broad current profile targets have low values of plasma internal inductance, l i, less than 0.4, near to the lower end of present NSTX operation. A key significance of this operation is that it approaches the purely current-driven ideal kink limit, which by definition exceeds the no-wall stability limit for all values of plasma normalized pressure (beta). In this regime, passive or active kink and resistive wall mode (RWM) stabilization is critical. Experiments on NSTX have recently approached this condition, evidenced by a significant reduction of the n = 1 no-wall stability limit computed by DCON. This limit drops from normalized beta of 4.2 – 4.6 at l i ~ 0.6, to 3.4 at li ~ 0.5, to below 2.8 for li ~ 0.4. Nevertheless, passive and active RWM control has produced high toroidal beta up to 28 percent, and normalized beta up to 6.5 (nearly double the no-wall limit), closely following a record normalized beta to li ratio of 13 between li = 0.4 - 0.5. Non-inductive current fraction reaches 0.5 in these high normalized current plasmas. However, the disruption probability of these plasmas increases significantly, with about half of the discharges suffering terminating instabilities. Alteration of n = 1 RWM control system parameters, plasma rotation profile, and the role of beta feedback is examined to potentially improve mode stability. Ion precession drift and bounce frequency resonance stabilization is examined for these plasmas and compared to the identified stabilization reduction at intermediate plasma rotation and higher l i [1,2].

[1] J.W. Berkery, et al., Phys. Rev. Lett. 104, 035003 (2010)

[2] S.A. Sabbagh, et al., Nucl. Fusion 50 , 025020 (2010)

*Work supported by U.S. DOE Contracts DE-FG02-99ER54524 and DE-AC02-09CH11466.


NSTX is Addressing Global Stability Needs for Maintaining Long-Pulse, High Performance Plasmas




to ITER

Physics Research Addressed Plasma operation at low plasma internal inductance, li Resistive wall mode (RWM) destabilization at high plasma rotation RWM active control enhancements / advances at low li Combined control systems to maintain <N>pulse at varied

Multi-mode RWM spectrum in high N plasmas

Papers: ppppppppp


Steady-State STs Targeted to Operate High BN/li

[1]: Peng, et al, PPCF 2005, Phase #3, 2 MW/m2 NWL

[2]: ARIES-ST

Common Features of Present & Future STs• High- and strong shaping.•N values at or above the no-wall limit. • Bootstrap fractions ≥50%. • Confinement ≥ H-mode scaling.• Comprehensive shape, profile and stability control.

Configuration Specific Features• Range of normalized currents.• Wide range of NBCD fractions.• Wide range of normalized

densities.

N

li(1)

IN

fGW

fBS

fNBCD

H98

NSTX

2.6

5.7

0.55

2.5

0.8

0.54

15

1.

NSTX-U

2.7

5.7

0.65

2.1

0.7

0.7

30

1.2

NHTX

3

5

0.6

3

0.45

0.7

0.3

1.3

ST-CTF1

3.1

4-6

0.35

4.5

0.28

0.5

0.5

1.5

ST-Demo2

3.5

7.5

0.25

6.7

0.8

0.96

0

1.3

S.P. Gerhardt (NSTX PAC-27)


NSTX is Addressing Global Stability Needs Furthering Steady Operation of High Performance Plasmas

RWM instability observed at intermediate correlates with kinetic stability theory

n = 1 RWM, N feedback control maintains high N at varied using n = 3 NTV profile modification

Stronger NTV braking at reduced E

Initial success of RWM state space controller at high N

Multi-mode RWM physics spectrum

profile control

Sufficient EP stabilization

Potential control compatibility

profile control impact

More flexibility of control coil placement

Determine RWM control impact

Sufficient EP stabilization needed at low

Potential control at low if EP stabilization insufficient

Further examine NTV at low



Physics addressed Future STs(NBI-driven, high )

ITER advanced scenarios (low )

Implications for


NSTX Database Plots – v2

BetaN vs. li (maximum values)


NSTX Database Plots

BetaN vs. li (pulse-averaged values)


NSTX Database Plots – v2 – li08



NSTX Database Plots



NSTX Database Plots

BetaN vs. li (pulse-averaged values)


Pressure peaking factor remains an essential component of high N operation

Broad pressure profile needed to maintain high N stability limit

•BetaN vs. Pressure peaking plot here


Characterization of Disruption Stats and Wtot variation here

Show improved disruption statistics and Wtot variation

Disruption Statistics

Wtot variation


Update this slide (use <betaN>, <betaT>, <betaN/li>


MISK calculations show reduced stability in low li target plasma as is reduced, RWM instability is approached

Stability evolves li increases in time as RWM

instability is approached, but remains low (li = 0.42)

MISK computation shows plasma to be stable at time of minimum li

Region of reduced stability vs. found before RWM becomes unstable (li = 0.49)

• Co-incident with a drop in edge density gradient – reduces kinetic stabilization

MISK application to ITER (advanced scenario IV) RWM unstable at expected rotation Only marginally stabilized by

alphas at N = 3

140132

t = 0.704s

stable

unstable

- BP9.00057 J. Berkery, et al.- Also, see poster for detail

experiment

RWM stability vs. (contours of w)

2.0

1.0

/exp


(Bp Feedback Phase Slide): Adjusting Bp sensor feedback phase around 180 degrees led to long-pulse, low li, high N/li

139347139515139516139517

Steady, high N/li Between 12

– 13

Low li state retained

180 deg202.5 deg157.5

Bpn = 1 (G)

Ip (MA)

N

li

N/li


0123456

0123456

-600-400-200

0200400600

02468101214

0 0.2 0.4 0.6 0.8 1.0 1.2sec

051015202530

135468135513

Shots:

N feedback combined with n = 1 RWM control to reduce N fluctuations at varied plasma rotation levels

Prelude to control Reduced by n

= 3 braking is compatible with N FB control

Steady N established over long pulse independent of

over a large range

Radial field sensors added to n = 1 feedback (2010) Full sensor set

further reduces n = 1 amplitude, improves control

135468135513

0.80.4 0.6 1.0 1.2t(s)

0.20.0

N

2

46

I RW

M-6 (

kA) 0.6

0

2

46

-0.6

PN

BI (

MW

) ~

q=

2

(kH

z) c

ore

(kH

z)

48

12

30

10

n = 3 brakingn = 1 feedback

0

20

0

q ~ 2 rotation

Core rotation

n = 3 errorcorrection


VALEN comparisons to NSTX PID feedback

(Probably won’t be enough time for this – perhaps a bullet at most, if the results are in)

Show that new PID feedback settings are consistent with theory Bp sensor feedback is consistent with (old) VALEN model

Consistent with new VALEN model? BR sensor feedback is consistent with VALEN model

VALEN comparisons


Include more RWM State-space controller results

New results / analysis / slides (possible ToDos) Improved diagram for feedback phase (show more phases?) Illustration of changing gains in experiment

Completed ideas included in talk Theoretical stability predictions Illustration of changing number of states in experiment

• Done for observer



Balancingtransformation

~3000+ states

Full 3-D model

…

RWMeigenfunction(2 phases,

2 states)

)ˆ,ˆ( 21 xx 3x̂ 4x̂ Nx̂truncate

State reduction (< 20 states)

State space feedback with 12 states

Controller can compensate for wall currents Including mode-induced current Examined for ITER

Successful initial experiments Suppressed disruption due to n

= 1 applied error field Best feedback phase produced

long pulse, N = 6.4, N/li = 13

- device R, L, mutual inductances- instability B field / plasma response- modeled sensor response

Katsuro-Hopkins, et al., NF (2007) 1157

00.20.40.60.81.01.2

amperes

01234567

-

0246810

Tesla

0100200300400500

amperes

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4sec

02468

140037140035


N

IRWM-4 (kA)

~q=2

(kHz)

Bpn=1 (G)

Ip (kA)

0.80.4 0.6 1.0 1.2t(s)0.20.0 1.4

1.00.5

06420840

400200

0

840

12

00.20.40.60.81.01.2

amperes

01234567

-

0246810

Tesla

0100200300400500

amperes

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4sec

02468

140037140035


N

IRWM-4 (kA)

~q=2

(kHz)

Bpn=1 (G)

Ip (kA)

0.80.4 0.6 1.0 1.2t(s)0.20.0 1.4

1.00.5

06420840

400200

0

840

12


RWM State Space Control – Theoretical Performance

text

Low N

input

2, 12 states

High N

input

Control at low plasma rotation

4.0 N4.5 5.0 5.5 6.0 6.5 7.0 7.5

100

101

102

103

104

(1

/s)


Passive growth

Idea

l Wal

l Lim

it

State

space

controller

(low input)

(high

input)


RWM State Space Control – Theoretical Performance

text

Low N

input

2, 12 states

High N

input

Control at low plasma rotation

ideal wall limitpassive growthinput 1: 12 statesinput 2: 12 states

4.0 N4.5 5.0 5.5 6.0 6.5 7.0 7.5

100

101

102

103

104

(1

/s) Proportional gain

control limit

Passive growth


Organization / Outline slides


Specifics

Talk constraints 25 minutes talk + 5 minutes discussion (8 more mins. than IAEA) 2010 IAEA had 14 slides (was tight): 1.214 min/slide Estimate 20 - 21 slides, plus backup 2001: 20 slides (simple slides – ok length) 2006: 16 slides (good length)


Outline - Topics

Outline - Topics Motivation – ST-CTF, ST Pilot Plant, ITER

• Maintenance of high beta state, with miminal fluctuation

• Active control needs to meet needs of high neutron flux devices (coils further back from device, or shielded)

• Outline: include both passive and active stabilization physics – and keys for how they extrapolate to future devices

Example of broad current profile target plasma (ST-CTF or ST-Pilot; NSTX-U) Illustration of stability space (li, BetaN) showing schematic limits

• Show NSTX database, with schematic limits superposed

• Show position of ST-CTF, ST-Pilot, NSTX-U, etc. on this plot

Illustration of stability space (li, BetaN) – ZOOMED in to low li

• Show recent low li plasmas as a different color on this plot Might be effective as an overlay plot, depending on where recent data / stable data lies on diagram

• Separate out stable plasmas vs. disruptions if possible

Ideal no-wall stability limit computation for trajectories on (li, BetaN) diagram

• Give margin over the n = 1 no-wall limit

Progress towards maintaining steady plasma stored energy at high beta

• Initial runs (2009) – high disruption probability – show statistics in bullets / stacked bar chart / plots on diagram

• Long-pulse shots at high betaN ELM-free, and no large Li buildup, no n = 1 rotating mode (with lithium)

• Improved PID feedback control (Bp and Br sensor results)

• state-space control

• beta feedback – at varied rotation

• Figures of merit: pulse avg betaN, std deviation

Passive stabilization physics

• Rotation and EP effects - (need equilibria for most recent results)

• Comparison of higher li to low li plasmas – difference in physical interpretation?

RWM control at high beta; considerations for burning plasma devices

• Multi-mode RWM physics, observations in NSTX


Outline – Slides I (WORKING VERSION) Outline – Slides (16 slides minimum , 20 slides maximum)

Title page Motivation – ST-CTF, ST Pilot Plant, ITER

• Maintenance of high beta state, with minimal fluctuation

• Active control needs to meet needs of high neutron flux devices (coils further back from device, or shielded)

• Outline: include both passive and active stabilization physics – and keys for how they extrapolate to future devices

Example of broad current profile target plasma (ST-CTF or ST-Pilot; NSTX-U) Low li plasma with RWM instability – 137722, or other (use IAEA slide directly? Good segway to MISK results) Illustration of stability space (li, BetaN) showing schematic limits

• Show NSTX database, with schematic limits superposed

• Show position of ST-CTF, ST-Pilot, NSTX-U, etc. on this plot

Illustration of stability space (li, BetaN) – ZOOMED in to low li

• Show recent low li plasmas as a different color on this plot Might be effective as an overlay plot, depending on where recent data / stable data lies on diagram

• Separate out stable plasmas vs. disruptions if possible

Ideal no-wall stability limit computation for (li, betaN) trajectories on (li, betaN) diagram

• Give margin over the n = 1 no-wall limit

Progress towards maintaining steady plasma stored energy at high beta

• Initial runs (2009) – high disruption probability – show statistics in bullets / stacked bar chart / plots on diagram

• Long-pulse shots at high betaN ELM-free, and no large Li buildup, no n = 1 rotating mode (with lithium)

Improved PID feedback control (Bp and Br sensor results) state-space control beta feedback – at varied rotation Figures of merit: pulse avg betaN, std deviation

(Continued on next page)


Outline – Slides II (WORKING VERSION)

Outline – Slides (16 slides minimum , 20 slides maximum) (Continued from prior page)

Passive stabilization physics

• Rotation and EP effects - (need equilibria for most recent results)

• Comparison of higher li to low li plasmas – difference in physical interpretation? Multi-mode RWM physics, observations in NSTX Multi-mode RWM physics, implications for ITER Summary (use format showing implications for future STs, ITER - worked well at IAEA)


Outline – Slides – Version 2 (IAEA) Outline – Slides (11 slides minimum , 13 slides maximum)

Title page Motivation – ST-CTF, ST Pilot Plant, ITER

• Have outline on this slide, or as a separate (very simple) slide?? NSTX device / geometry slide RWM instability / RFA at high plasma rotation

• Instability at intermediate and high rotation – low rotation “threshold” not adequate for stability Consequences for an ST-CTF / Pilot Plant, and ITER

• Show RFA results here from recent XP1020 as well Passive stabilization physics – NSTX and MISK code

• MISK physics – intro slide Passive stabilization physics – NSTX rotation / collisionality (thermal particles)

• Rotation and collisionality effects – contour plot

• Clearly state physics implications for ITER and ST-CTF – importance of new results vs. old (low) crit.rotation Unification of devices using new model (MISK)

• DIIII-D: comparison of energetic particle fraction / stability margin due to EPs vs. NSTX

• JT-60U: (mention in a bullet on this slide)

• ITER: BULLET HERE – advetrize full slide that will appear on poster Progress towards maintaining steady plasma stored energy at high beta

• As default, use slide with n = 3 EFC, n = 1 FB, betaN control

• Improved PID feedback control; state-space control; beta feedback – at varied rotation

• Figures of merit: pulse avg. betaN, std. deviation The role of NTV physics at low nu_i/OmegaE, and low OmegaE - Superbanana plateau regime in NSTX

• Low OmegaE results – superbanana plateau in NSTX

• Optional: results for NTV offset rotation, change in rotation damping vs. collisionality, etc. RWM state space control

• RESERVE the theoretical growth rate plot for the POSTER and PAPER

• Need to DEFINE state space control / NSTX especially well suited to test / connect to ITER

• First experimental results RWM control at high beta; considerations for burning plasma devices (I)

• Multi-mode RWM physics, expectations in NSTX – NSTX mmVALEN mode spectrum RWM control at high beta; considerations for burning plasma devices (II)

• Addition of differential rotation – change in VALEN multi-mode spectrum, rot. speed; observations in NSTX Summary


Some IAEA FEC 2010 slides follow


NSTX is Addressing Global Stability Needs for Maintaining Long-Pulse, High Performance Plasmas




to ITER

Physics Research Addressed Resistive wall mode (RWM) destabilization at high plasma rotation RWM active control advancements Combined control systems to maintain <N>pulse at varied

Physics of 3D fields to control plasma rotation Multi-mode RWM spectrum in high N plasmas

Papers: ppppppppp



RWM instability observed at intermediate correlates with kinetic stability theory

n = 1 RWM, N feedback control maintains high N at varied using n = 3 NTV profile modification

Stronger NTV braking at reduced E

Initial success of RWM state space controller at high N

Multi-mode RWM physics spectrum

profile control

Sufficient EP stabilization

Potential control compatibility

profile control impact



Sufficient EP stabilization needed at low

Potential control at low if EP stabilization insufficient

Further examine NTV at low



Physics addressed Future STs(NBI-driven, high )

ITER advanced scenarios (low )

Implications for


Rotation profile at RWM marginal stability altered by varying energetic particle content

Ip, Bt altered keeping q fixed in experiment

Fast ion density increases with increased Ip

Indicated by fast ion D diagnostic

Range of TRANSP fast/tot 17% - 31%

General reduction of RWM marginal profile as Ip increased

Rotation profiles at marginal stability

Relative fast ion density profiles

J.W. Berkery, et al., Phys. Plasmas 17 (2010) 082504

NSTXNSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low li Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.) 67November 9th, 2010 6767

Model of kinetic modifications to ideal stability can unify RWM stability results between devices

NSTX Less EP stability: RWM can cross

marginal point as is varied

DIII-D More EP stability (~ 2x NSTX):

RWM stable at all

RWM destabilized by events that reduce EP population

ITER (advanced scenario IV) RWM unstable at expected rotation Only marginally stabilized by alphas

at N = 3

Stability overpredicted with EPs – model development continues Improve NBI anisotropic distribution Examine effects originally thought

small

H. Reimerdes, et al., paper EXS/5-4

NSTX

DIII-D

calculation with EPs

unstable

thermal ions

energetic particles (EPs)

NSTXDIII-D (rescaled)

See poster (EXS/5-5)γτw ~ 0.1

NSTX

experiment

See poster (EXS/5-5)


Additional Slides



RWM instability observed at intermediate plasma rotation correlates with kinetic stability theory Theory of kinetic modifications to ideal stability may unify RWM stability

results between devices

ITER advanced scenario 4 requires EP stabilization at expected

n = 1 RWM feedback control combined with new N feedback control shows regulation of high N at varied plasma rotation levels

Compatible with plasma rotation control by non-resonant 3D fields

Stronger non-resonant NTV braking observed at reduced E

Theoretically expected (superbanana plateau regime)


Potential for greater flexibility of RWM control coil placement for burning plasma devices

Computed multi-mode RWM spectrum at high N shows significant amplitude in higher order modes


Energetic particles are stabilizing to RWM; computed effect is smaller in NSTX when compared to DIII-D

Smaller energetic particle (EP) fraction in NSTX Less stability due to EPs

Scaled Wk from MISK shows larger stabilization effect due to EPs in DIII-D

H. Reimerdes, et al., paper EXS/5-4


Advancements in MISK stability model continue

Electrostatic effect Additional anisotropic term

Centrifugal destabilization Other possibilities:

[B. Hu et al., Phys. Plasmas 12, 057301 (2005)]

In addition to present anisotropy effects on δWK, when f is anisotropic an additional term arises that is proportional to :

– Inclusion of plasma inertia term in the dispersion relation

– Effect of poloidal rotation on ωE (small)– Use of a Lorentz collisionality model instead of

current ad-hoc inclusion of collisionality

The electrostatic component of the perturbed distribution function contributes to δW. (expected to be small).

This fluid force term is usually neglected, but it is always destabilizing, and could be important if the plasma rotation Mach number is significant, or for alpha particles rotating at higher frequency ~ ω*α.

(significant for NSTX in core, not edge)

progress toward stabilization of low internal inductance spherical torus plasmas in nstx s.a....

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